The asymptotic almost sure (a.sで)representation of sample quantiles for independent and identically distributed random variables was firstly established by Bahadur[1]。Kiefer[5,6]obtainedfurther developments on this line and also investigated the a。s.representation of quantile process. Here we remark that the representation of sample quantiles in the sense of in probability was obtained first of all by Okamoto [7]。The extensions of Bahadur's by relaxing the assumption of independence of the basic random variables have been studied by a number of authors. Especially, Sen[10]obtained completely analogous results to Bahadur's one for stationaryφ・mixing processes. The object of the present paper is to show that the Bahadur representation holds, but with a slightly differentorder of the remainder term, for stationary sequences of strong mixing random variables。W'e also consider the Bahadur representation for absolutely regular processes and the a.s.representation of quantiie processes for $J-mixing and strong mixing processes。 LetiXn, n≧1} be a strictlystationary sequence of random variables defined on a probability space (2,J,P)。We shall say that the sequence {xj isφ-mixing if